Your GVWR is the max of the trailer, including the hitch. 9700 is the max for your rig. With four tires on the ground, most manufacturers use that weight or close to it, equally split among the tires so a tire with a rating of just under 2400 is about right. The hitch will take another 900 pounds off so each tire will be loaded at about 2200 or so in a perfectly balanced world.
The CCC is key, everything you put in/on must be accounted for. Not sure about the FR Salem, but GDRV provides a weight sheet for each unit. Add propane, battery fresh water and then everything else you carry for the family, if it is under the GVWR, there should not be an issue - suggest you run it across a scale to really know.